The accretion effect with the dominant modes has been studied in Refs. [1]}, [2]}. Below we first interpret the results in Ref. [1]}, which considers only the \(\lbrace 0,1,1\rbrace \)  mode. In their calculation, the mass accretion is conservatively assumed to be a fraction of the Eddington rate,
\(\dot{M}_\text{ACC} \equiv f_\text{Edd} \dot{M}_\text{Edd} \sim 0.02 f_\text{Edd}\frac{M(t)}{10^6 M_\odot } M_\odot \text{yr}^{-1},\) 
